4.2 Mendel, Segregation and Punnett Grids

Gregor Mendel controlled pollination of pure-breeding pea plants and counted thousands of offspring. When he crossed parents differing in one characteristic, the F1 displayed only one parental phenotype. Self-pollination of F1 restored the hidden phenotype in F2 at about 3:1. The missing characteristic had not blended away; a discrete hereditary factor remained present but masked.

Modern genetics explains the pattern with paired alleles. A dominant allele has the same phenotype in homozygous and heterozygous states under stated conditions. A recessive allele affects phenotype only without the dominant allele. The two alleles segregate during meiosis and fertilization restores a pair. Mendel inferred this without knowing about chromosomes or DNA.

Define allele symbols and parental genotypes, list each distinct haploid gamete, and combine them in a grid. Every inner cell represents one possible fusion. Count genotypes first, then translate them using the dominance rule. A dominant-looking parent may be homozygous or heterozygous; phenotype alone does not decide.

For $Aa\times Aa$, each parent makes A and a gametes equally. Zygote probabilities are $1/4\,AA$, $1/2\,Aa$ and $1/4\,aa$, giving 3:1 phenotypes under complete dominance. The test cross $Aa\times aa$ gives 1:1. Crossing an unknown dominant-phenotype individual with a recessive tester can reveal whether the unknown produces a gametes.

Each fertilization is an independent event if one outcome does not affect the next. Multiplication gives the probability of independent events all occurring; addition combines mutually exclusive routes. Small families can depart sharply from expectation, while large samples usually approach the probability ratio. Mendel's large counts were therefore central evidence.

A Punnett grid assumes equal gamete production and survival, random fertilization and equal zygote survival unless stated otherwise. Linkage, lethal genotypes or selection can shift observed ratios. A discrepancy invites investigation rather than proving the grid wrong.

Mendel's stem-height cross produced 787 tall and 277 short F2 plants, a ratio of about 2.84:1 rather than exactly 3:1. Other characteristics gave different small departures. The agreement across several large experiments mattered more than perfect numerical identity. His result also rejected blending inheritance: if parental information had merged irreversibly into an intermediate, the short phenotype could not have reappeared unchanged in F2.

Homozygous means carrying identical alleles at a locus, such as AA or aa; heterozygous means carrying different alleles, Aa. These terms apply to genotype, not phenotype. A dominant-phenotype individual may be either AA or Aa, while a recessive phenotype fixes aa in the simple complete-dominance model. The recessive phenotype is therefore often more informative even though the recessive allele is not necessarily rare.

A cross should show why each gamete is possible. An AA parent produces only A gametes because either homologue supplies A. An Aa parent produces A and a because homologues separate. Repeating identical gametes around a Punnett grid can be visually convenient, but it does not create new gamete types. Probability comes from the proportion of gametes, not from how many times a symbol is written.

Single-nucleotide polymorphisms provide abundant markers for following inheritance. A SNP between genes may have no functional effect but remain physically associated with a nearby disease allele, especially when recombination between the sites is rare. Researchers can therefore detect statistical association without the marker causing disease. Association narrows a genomic region; experiments are still needed to identify the causal sequence and mechanism.